Transfer line exchanger

ABSTRACT

The present invention provides a transfer line exchanger which is optimized for one or more objective functions of interest such as pressure drop, erosion rate, fouling, coke deposition and operating costs. The transfer line exchanger is designed by computer modeling a transfer line exchanger in which the cross section of flow path is substantially circular and modeling the operation of the transfer line under industrial conditions to validate the model design and its operation. Then iteratively the model design is deformed and the operation of the deformed part is modeled and compared to values obtained with other deformed models until the value of the objective function is optimized (e.g. at an extreme) or the change in the objective function is approaching zero.

REFERENCE TO RELATED APPLICATION

This application is a divisional of U.S. patent application Ser. No.14/082,522 filed on Nov. 18, 2013 entitled “Transfer Line Exchanger”which is herein incorporated by reference in its entirety.

BACKGROUND OF THE INVENTION

In the cracking of paraffins to produce olefins, and particularly alphaolefins, a feed stock, for example, a lower paraffin such as ethane ornaphtha, is heated to a temperature of at least about 850° C., or fromabout 900° C. to about 1000° C. In the process, the molecules in thefeed stock lose hydrogen and become olefins. This process takes place inthe heater coils inside the furnace in the radiant box of the ethylenecracker. The hot gases leaving the furnace are quickly fed to a quenchexchanger. The line from the exit of the furnace tubes to the quenchexchanger tube sheet or cooling section entrance is a transfer line. Dueto the configuration of most plants the transfer line contains an elbowhaving, for example, about a 90° bend. The transfer line may include adiffuser to transition the diameter of the flow from that of the furnacepipe or tube to the diameter of the tubesheet of the quench exchanger(e.g., the external surface of the quench exchanger). There may also beseveral sections or fittings in the transfer line so that it may not bea unitary piece of pipe. In the quench exchanger, the gasses are quicklycooled to a temperature below which they will no longer react.

FIELD OF THE INVENTION

To date, the transfer lines have been circular in cross-section. Theconsideration of the cost of manufacture relative to efficiency of thetransfer line, in terms of pressure, drop and erosion rate has beenlargely weighted to minimize the cost of manufacturing. Hence, thetransfer lines have circular tubular pipes. With the increase in theprice of feedstocks both for the cracking process and the furnace andthe concern about greenhouse gas emissions, the weighting of the factorsin the design of a transfer line exchanger is starting to move towardthe efficiency of the process. Several factors to be considered in theefficiency of the furnace include the pressure drop across (i.e., alongthe length of) the transfer line, the erosion rate of the transfer lineand the degree of recirculation of the flow which relates to fouling(e.g., coke deposition).

U.S. Pat. No. 6,041,171 issued Mar. 21, 2000 to Blaisdell et al.discloses a method for designing a material handling system. A computeris used to select parts from a catalogue or inventory of parts. Theprogram is more directed at assembling pre-existing parts than designingnew parts.

U.S. Pat. No. 6,778,871 issued Aug. 17, 2004 teaches a method to usecomputer assisted design (CAD) to initially generate drawings for a pipenetwork. The system “designs” and “fabricates” pipe networks but itappears that this is based on standard pipe sizes (Col. 4 line 50). Thesystem does not appear to design “custom” pipe or a custom elbow.

U.S. Pat. No. 7,398,193 issued Jul. 8, 2008 to Araki et al. discloses amethod to “estimate” the wall thinning of a pipe at a “not measuredlocation” to plan piping maintenance work. The reference is helpful indemonstrating that there are computer programs to estimate “wallthinning”. The process is based on actual measurements of pipe erosionand modeling the fluid flow throughout the entire pipe network or systemto predict the rate of wall thinning at a point distant from the actualmeasurement. This is then used to predict the locations of potentialpipe failure and to schedule maintenance of the pipe network to minimize“down time”. Again, the program is not directed to designing individualcomponents for the pipe network to minimize pressure drop and erosion.

There are a number of patents in the names of Oballa, and Benum assignedto NOVA Chemicals relating to surfaces on furnace tubes and methods formaking them including U.S. Pat. No. 6,824,883 issued Nov. 30, 2004; U.S.Pat. No. 6,899,966 issued May 31, 2005; and U.S. Pat. No. 7,488,392issued Feb. 10, 2009.

Applicants have been able to determine there is no art suggesting anon-circular cross section for a transfer line.

A need exists for a transfer line for an olefin cracker which isfabricated to minimize any one of, or, combinations of, pressure drop,fouling, recirculation, erosion in the transfer line and cost(operating, capital or both).

SUMMARY OF THE INVENTION

The present invention relates to the transfer line in furnaces forcracking paraffins to olefins, particularly for the production ofethylene.

In one embodiment, the present invention provides a transfer line froman olefins cracking furnace to a quench exchanger, said transfer linehaving an internal flow passage having a continuously smooth anddifferentiable perimeter and centerline and a smoothly varyingcross-section along the flow passage such that in the about 5% of theflow passage from the inlet and the outlet, the ARQ is from about 1.0 toabout 1.02 and over the remaining about 90% of the length of the flowpassage not less than about 5% of the flow passage has an ARQ which isfrom about 1.02 to about 1.5.

In a further embodiment, the ARQ over said remaining about 90% of thelength of the flow passage does not change by more than about 7% over anabout 5% length of the flow path.

In a further embodiment, the ARQ at one or more sections over saidremaining about 90% of the length of the flow passage is from about 1.02and about 1.30.

In a further embodiment, the ARQ over said remaining about 80% of thelength of the flow passage does not change by more than about 5% over anabout 5% length of the flow path.

In a further embodiment, the calculated total pressure drop across thetransfer line is decreased by not less than about 10% compared to thecalculated pressure drop for transfer line having an ARQ along itslength from about 1.00 to about 1.02.

In a further embodiment, the ARQ at one or more sections over saidremaining about 80% of the length of the flow passage is from about 1.02and about 1.15.

In a further embodiment, the normalized calculated erosion rate of thetransfer line is decreased by not less than about 10% compared to thenormalized erosion rate for transfer line having an ARQ along its lengthfrom about 1.00 to about 1.02.

In a further embodiment, the transfer line has an increasing crosssectional area in the direction of flow such that the angle between thetransverse normal vector and the pipe walls range from about 0° to about85°.

In a further embodiment, the transfer line has, a smooth curve in itslongitudinal direction which although may change rapidly, may notinclude abrupt, sharp changes of internal section (steps), and has aradius of curvature on the internal surface of the curve from unbound(straight) to half the vertical of the section radius. For example, theradius of curvature on the internal surface of the curve may be fromabout 1 internal pipe diameters to about 5 internal pipe diameters.

In a further embodiment, the transfer line comprises from about 20 toabout 50 weight % of chromium, about 25 to about 50 weight % of Ni, fromabout 1.0 to about 2.5 weight % of Mn, less than about 1.0 weight % ofniobium, less than about 1.5 weight % of silicon, less than about 3weight % of titanium and other trace metals and carbon in an amount lessthan about 0.75 weight % and from about 0 to about 6 weight % ofaluminum.

The present invention provides a method to optimize one or more of theoperating characteristics selected from pressure drop, erosion rate,fouling rate, and cost (capital, operating or both) of a fixedindustrial flow path defined by a continuous metal and/or ceramicenvelope, comprising:

1. building a computational model comprising not less than about 5,000,or for example about 10,000 to about 100,000, or, for example, more thanabout 100,000, computational cells for all or a portion of the flowchannel from about 5% of the length of the flow channel downstream ofthe inlet to from about 5% of the length of the flow channel upstream ofthe outlet of the initial design of said industrial flow path;

2. using computer software that solves the fundamental laws of fluid andenergy dynamics for each cell simulating and summing the results of theoperation of the model design from step 1 under the industrial pressure,temperature, and flow rate conditions of operation to verify one or moreobjective functions of interest (e.g., pressure drop, erosion rate,fouling, coke deposition and cost) to match operating conditions;

3. iteratively,

a) deforming said computational model comprising not less than about5,000 computational cells so that the resulting ARQ of one or moresections of the flow path is greater than about 1.02;

b) applying the same computer software as in step 2, that solves thefundamental laws of fluid and energy dynamics for each cell simulatingand summing the results of the operation of the deformed model from step3a) under the industrial pressure, temperature, and flow rate conditionsof operation used in step 2 to predict one or more objective functionsof interest (e.g., pressure drop, erosion rate, fouling, coke depositionand cost) for the operation of the deformed model;

c) storing the predicted results from step 3b);

d) using some or all of the stored results from step 3c) with anoptimization algorithm to estimate a deformation that will improve theobjective function;

e) repeating steps a), b), c), and d) until one or both of the followingconditions are met:

-   -   i) the objective function of interest goes through a beneficial        local extrema; or    -   ii) the rate of change of all of the functions of interest        starts to approach 0.

BRIEF DESCRIPTION OF THE DRAWINGS

The features, benefits and aspects of the present invention are bestunderstood in the context of the attached figures in which like parts orfeatures are designated by like numbers.

FIG. 1 shows different cross sections of a flow path having an ARQgreater than 1.

FIG. 2 shows a series of overlays of equal perimeter ellipses havingdifferent ARQ equal to or greater than 1.

FIG. 3 is an isometric view of a transfer line of the prior art.

FIG. 4 is a sectional view along the flow path of FIG. 3 and crosssections A, B, and C.

FIG. 5 is an isometric view of a transfer line in accordance with thepresent invention.

FIG. 6 is a sectional view along the flow path of FIG. 5 and crosssections at A′, B′, and C′.

FIG. 7 is an isometric view of a transfer line designed in accordancewith example 1.

FIG. 8 is a sectional view along the flow path of FIG. 7 and crosssections at A″, B″, C″, D″, E″, F″ and G″.

DETAILED DESCRIPTION

Other than in the operating examples or where otherwise indicated, allnumbers or expressions referring to quantities of ingredients, reactionconditions, etc., used in the specification and claims are to beunderstood as modified in all instances by the term “about”.Accordingly, unless indicated to the contrary, the numerical parametersset forth in the following specification and attached claims areapproximations that can vary depending upon the properties that thepresent invention desires to obtain. At the very least, and not as anattempt to limit the application of the doctrine of equivalents to thescope of the claims, each numerical parameter should at least beconstrued in light of the number of reported significant digits and byapplying ordinary rounding techniques.

Notwithstanding that the numerical ranges and parameters setting forththe broad scope of the invention are approximations, the numericalvalues set forth in the specific examples are reported as precisely aspossible. Any numerical values, however, inherently contain certainerrors necessarily resulting from the standard deviation found in theirrespective testing measurements.

Also, it should be understood that any numerical range recited herein isintended to include all sub-ranges subsumed therein. For example, arange of “1 to 10” is intended to include all sub-ranges between andincluding the recited minimum value of 1 and the recited maximum valueof 10; that is, having a minimum value equal to or greater than 1 and amaximum value of equal to or less than 10. Because the disclosednumerical ranges are continuous, they include every value between theminimum and maximum values. Unless expressly indicated otherwise, thevarious numerical ranges specified in this application areapproximations.

All compositional ranges expressed herein are limited in total to and donot exceed 100 percent (volume percent or weight percent) in practice.Where multiple components can be present in a composition, the sum ofthe maximum amounts of each component can exceed 100 percent, with theunderstanding that, and as those skilled in the art readily understand,that the amounts of the components actually used will conform to themaximum of 100 percent.

As used in this specification, “relatively smoothly” in relation to theARQ means the quotient does not change by more than about 7% over anabout 5% length of the flow path.

As used in this specification, “smooth” in relation to the perimeter ofthe flow passage means the perimeter at an angle perpendicular to theflow is a differentiable continuous smooth line (i.e., havingsubstantially no kinks or discontinuities). In one embodiment, theperimeter of the flow passage will not be a geometric shape havingstraight sides and “corners” or “angles” such as a square, aparallelogram or a triangle. Rather, the perimeter of the flow passageis defined by a continuous smooth curved line.

As used in this specification, “smooth” in relation to the center lineof the flow passage means the center line of the flow passage is adifferentiable continuous smooth line (i.e., having substantially nokinks or discontinuities). While the center line of the flow passage maychange rapidly, it may not include abrupt, sharp changes of internalsection (steps).

As used in this specification, “building a computational model” meanscreating a virtual three dimensional geometric model of the transferline exchanger and filling it with a three dimensional computationalmesh to create cells (e.g., at least about 5,000 cells, or greater thanabout 5,000 cells, or about 10,000 cells to about 100,000 cells, orgreater than about 100,000 cells).

“ARQ” is defined as the ratio of aspect ratio (AR) to isoperimetricquotient (Q) of a section or segment of the flow passage perpendicularto the direction of flow (AR/Q). The “aspect ratio” (AR) is defined asthe ratio of long to short side of the smallest-area rectangle intowhich a particular section can be circumscribed. This ratio, for thecase of a convex ovoid section symmetric about one axis, is equal to theratio of the major chord to minor chord. The major chord is the lengthof the longest straight line between two points in the perimeter of aclosed section which may or may not cross the centroid of the section.The minor chord for such a section is the longest distance perpendicularto the major chord between two points along the perimeter of thesection. It will appear clear to those skilled in the art that thusdefined, the aspect ratio is greater than one.AR=Long/Short

The “isoperimetric quotient” is defined as four times Pi (π) times theArea of the section of the flow path divided by the square of thatsection's perimeter. At a cross section of the flow path if the area ofthe cross section is A and the perimeter is L, then the isoperimetricquotient Q, is defined by

$Q = \frac{4\pi\; A}{L^{2}}$

The isoperimetric quotient is a measure of circularity. This isillustrated in FIG. 1 and FIG. 2.

A “circle” is a cross-sectional shape with an isoperimetric quotient ofone, and other cross-sectional shapes have an isoperimetric quotientless than one.

Since the ARQ ratio is the aspect ratio (AR) divided by theisoperimetric quotient (Q) and as defined AR is greater than one and Qis less than one, ARQ is also greater than one and greater than or equalto the aspect ratio.

FIGS. 1 and 2 demonstrate that even an ARQ near but not equal to 1 canbe noticeably non-circular.

Sample calculation of an ARQ ratio:

An ellipse with a major radius “a” and a minor radius “b” has a crosssectional area A=π*a*b. The perimeter of such an ellipse can beapproximated by Ramanujan's formula which states the perimeter of anellipse being approximately:L≈π[3(a+b)−√{square root over ((3a+b)(3b+a))}]

For a particular example of an ellipse having a major radius “a” equalto four times the minor radius “b”, it would have an Area A=4*π*b². Thisfour-to-one ellipse has a perimeter LL≈π[3(5b)−√{square root over ((12b+b)(3b+4b))}]L≈π[15b−√{square root over (91b ²)}]≈5.461πb

So a four-to-one ellipse has an isoperimetric quotient Q equal

$Q \approx \frac{16\pi^{2}b^{2}}{29.822\pi^{2}b^{2\;}} \approx 0.537$

And since the aspect ratio of this section is 4, the ARQ of such asection is 7.45

In comparison, standard pipe has an out-of round tolerance of plus orminus about 1.5% and as such, the maximum ARQ of a nominally roundsection is approximately 1.0151.

FIG. 3 is an isometric drawing of a prior art transfer line up to thetubesheet of the transfer line exchanger. The exchanger comprises aninlet 1, an elbow (or bend) 2, a body 3, a diffuser 4, and an outlet orexit 5. The hot gas from the cracker enters at the inlet 1, the smallercircular end of the transfer line, passes through the elbow 2, the body3, the diffuser 4 and passes through the exit 5 at the broader or flaredend of diffuser end 4.

In FIG. 4, cross sections are shown at A-A, B-B and C-C. In sometransfer line exchangers, the flow path is circular along its entirelength albeit expanding and the ARQ along the transfer line isessentially 1 (e.g., from about 1.0 to about 1.02).

In one embodiment, the cross sectional area of the flow path variessmoothly from a minimum to a maximum area along the length of thetransfer line exchanger in the direction of flow of the gas, but thecross-sections are substantially round with an ARQ of about 1, otherthan by unintentional variations of tolerance plus or minus about 2%(maximum ARQ of about 1.02). In one embodiment, the walls of thediffuser are diverging to convert momentum energy into pressure. It alsoallows for the connection from a smaller diameter flow passage (e.g.,the furnace tube) to the larger diameter of the heat exchangertubesheet. The angle of the taper along the center line of the flow pathis the angle between a line normal to the cross section and the flowpath walls. For maximum pressure recovery, the angle will be betweenabout 0° and about 15°, or between about 3° and about 10°, or betweenabout 4° and about 7°. However, as this results in long transitionregions, larger expansion angles may be used to maintain a shorter, lesscostly heat exchanger entrance. Pressure loss, fouling and erosion maybe increased in this case.

In one embodiment, the transfer line has a smooth curve in itslongitudinal direction, the elbow which may change rapidly but does notinclude abrupt or sharp changes of internal section, and has a radius ofcurvature on the internal surface of the curve from unbound (straight)to half the vertical of the section radius. In a further embodiment, thetransfer line has a smooth curve in its flow direction which has aradius of curvature on the internal surface of the curve from about 1internal pipe diameters to about 5 internal pipe diameters.

FIG. 5 is an isometric view of a transfer line, in accordance with oneembodiment of the present invention, comprising an inlet 1′, an elbow(or bend) 2′, a body 3′, a diffuser 4′, and an exit 5′. The hot gas fromthe cracker enters at the inlet 1′, the smaller circular end of thetransfer line, passes through the elbow 2′, body 3, the diffuser 4′, andexits at the exit 5 at the broader or flared end of the diffuser. Theexit 5′ of the diffuser is circular or substantially circular.

FIG. 6 shows sectional views of transfer line in accordance with oneembodiment of the present invention. The cross sections at A′-A′, B′-B′,and C′-C′ as well as the inlet and outlet are also shown. In someembodiments, the cross sections A′-A′, B′-B′ and C′-C′ in FIG. 6 are atthe same or comparable location as A-A, B-B and C-C in FIG. 4. The crosssection at the inlet 1 and exit 5 of the transfer line exchanger aresubstantially circular. However, the cross sections as A′-A′, B′-B′,C′-C′ and D′-D′ are not circular and have an ARQ substantially higherthan 1.

In this embodiment the ARQ varies smoothly from about 1 at either end(inlet 1 and exit 5 (round furnace pipe connected to a round tubesheet))but reaches a maximum non-roundness with a maximum ARQ of about 1.39.

The shape of the cross section of the flow path may be elliptical,ovoid, segmented or asymmetric in nature. The area of the cross-sectionmay also be held constant, increase or decrease according to thefunction to be achieved. A twist may optionally be imposed on adjacentcross sections either by means of interior swirling vanes or beads(e.g., a welded bead on the interior of the pipe) within the transferline exchanger or by the bulk twisting of the cross sections relative toeach other.

However, it should be noted that different shapes may have a comparableARQ and that a low change in the quotient may in fact result in asignificant change in the cross section shape of the flow path such asfrom a near ellipse to a “flattened egg shape.” This is demonstrated inFIGS. 1 and 2. In some embodiments, an about 1% change in ARQ can have aprofound effect on the flow characteristics as indicated by pressuredrop, for example.

In one embodiment, the cross section of the transfer line exchangerwithin the last about 5% of the flow path from the inlet and exit (oroutlet) of the transfer line exchanger have an ARQ approaching unityfrom above; for example, from about 1.02 to about 1.0, or from about1.01 to about 1.

In one embodiment, the remaining about 90% of the flow path has one ormore sections where the ARQ is from about 1.02 to about 1.50, or fromabout 1.02 to about 1.3, or from about 1.02 to about 1.12. The interiorof the flow path is “smooth” in the sense that the change in the ARQ, inabout 5% sections of the remaining flow path, does not change by morethan about 7%, or less than about 5%.

The shape of the cross sections of the flow path is optimized to obtaina local beneficial minimum or maximum (known collectively as “extrema”)of an objective function. Such objective function may be any parameteraffecting the economics of the operation of the transfer line,including, the cost (capital and or operating), itself include but isnot limited to pressure drop, erosion rate of the fluid-contactingsurfaces, weight of the component, temperature profile, residence timeand rate of fouling (or coke deposition).

There are a number of software applications available which are usefulin the present invention. These include SOLIDWORKS software for thecreation and parametric manipulation of the flow geometry, ANSYSMECHANICAL software for the calculation of material stress and ANSYSFLUENT software to determine the flow pattern, pressure drop and erosionrate used in calculating the objective function corresponding to aparticular geometry.

Procedurally, one way to find a local objective function extremum is bysequentially applying a small perturbation to a parameter affecting theshape of the transfer line and determining the resulting value of theobjective function by either analytical techniques, experiments ornumerical computation. A deformation parameter is defined as a valuewhich can be uniquely mapped to a change in geometry by means ofscaling, offsetting or deforming any or all of the sections in adeterministic fashion. Each parameter may also be bounded to preventgeometric singularities, unphysical geometries or to remain within theboundaries of a physical solution space. After each of a finite andarbitrary number of parameters has been perturbed, any one of a seriesof mathematical techniques may be used to find the local extremum. Inone such technique, a vector of steepest approach to the objectivefunction extremum is determined as a linear combination of parameterchanges. The geometry is progressively deformed in the direction ofsteepest approach and the value of the objective function determined foreach deformation until a local extremum is found. The process is thenrestarted with a new set of perturbations of the parameter set. Othertechniques that may be used to advance, the search for a local extremuminclude Multi objective genetic algorithms, Metamodeling techniques, theMonte Carlo Simulation method or Artificial Neural Networks.

For example, a model of the original design is built. That is a threedimensional finite model of the transfer line is created. The model mayinclude the internal flow passage (void) within the transfer lineexchanger. The model may also include the external surface of thetransfer line exchanger. The model may then be divided into (or filledwith) cells, for example, about 5,000 cells, or at least about 5000cells, or from about 10,000 to about 100,000 cells, or, for example,more than about 100,000 cells (e.g., about 150,000, or about 200,000, orabout 250,000, or about 500,000). To some extent, this is dependent oncomputing power available and how long it will take to run the programsfor each deformation of the original model. There are a number ofcomputer programs which may be used to build the original model such as,for example, finite element analysis software (e.g., ANSYS Mechanical).

Then the model needs to be “initialized”. That is a fluid dynamics andenergy (of mass, energy and momentum, etc.) dynamics computer program isapplied to each cell of the model to solve the operation of that cell atgiven operating conditions for the transfer line exchanger (e.g., massof gas passing through the transfer line exchanger, flow velocity,temperature, and pressure, erosion rate, fouling rate, recirculationrate, etc.) to calculate one or more objective functions. The sum of theresults of each cell operation describes the overall operation of thetransfer line exchanger. This is, run iteratively until the model andits operation approach, or closely match, actual plant data. Generally,the model should be initialized so that for one or more of objectivefunctions of the simulation is within about 5%, or within about 2%, orwithin about 1.5% of the actual plant operating data for that objectivefunction of the transfer line exchanger. One fluid and/or energydynamics program which is suitable for the simulation is ANSYS FLUENTsoftware.

Once the design of the transfer line and its operation is initialized,the model of the transfer line is iteratively deformed, for example, ina small manner but incremental manner and the simulated operation of thedeformed part is run to determine the one or more objective functionsfor the deformed transfer line exchanger (for the cells and the sum ofthe cells or even cells in specified location or regions (at theinternal radius of curvature of a bend). For example, the deformation isapplied to all of part of the flow channel of the transfer lineexchanger within about 5% of the flow channel downstream of the inlet toabout 5% of the flow channel upstream of the exit (i.e., about 90% ofthe transfer line is available for deformation). In some instances, thedeformation may occur in one or more sections or parts within about 10%of the flow channel downstream of the inlet to about 10% of the flowchannel upstream of the exit (i.e., about 80% of the transfer line isavailable for deformation). While the deformation could be applied tothe whole length of transfer line available for deformation it may beuseful to apply the deformation to sections or portions of the transferline. For example, the last or first half, third or quarter orcombinations thereof could be deformed. The results (e.g., one or moreobjective functions and the sum of each such objective function) of thesimulated operation of the deformed transfer line exchanger are storedin the computer.

The deformation of the transfer line may be accomplished by applying afurther computer program to the design which incrementally deforms thepart. One such commercially available deformation and optimizationsoftware is sold under the trademark Sculptor. However, one may use aneural network to optimize the location and degree of deformation tospeed up or focus the iterative process.

The stored calculated objective function(s) for the operation of thedeformed transfer line are then compared until either:

1) an extrema of one or more objective functions is reached; or

2) the rate of change in the one or more objective functions isapproaching zero.

More generally, the present invention provides a method to optimize oneor more of the operating characteristics of a fixed industrial flow pathdefined by a continuous metal envelope, selected from pressure drop,erosion rate, and coke deposition rate comprising:

1. building a numerical model comprising not less than about 5,000, or,for example, more than about 100,000, computational cells of the portionof the flow channel, for example, from about 5% of the flow channeldownstream of the inlet and to about 5% of the flow channel upstream ofthe outlet (e.g., about 90% of the of the flow channel of the transferline) of the initial design;

2. simulating (on a computational cell level and summed) the operationof the model design from step 1 using fluid and energy dynamics softwareunder the industrial pressure, temperature, and flow rate conditions ofoperation to numerically determine one or more of the functions ofinterest (pressure drop, erosion rate, fouling rate and cost (capitaland operating)) approach (within about 5%) or match actual operatingconditions;

3. iteratively,

a) deforming said numerical model comprising not less than about 5,000computational cells by deforming the geometry such that the resultingARC) of the section is materially greater than about 1.02;

b) simulating the operation of the deformed model under the plantoperating conditions used in step 2 to determine one or more objectivefunctions of interest (e.g., pressure drop, erosion rate, fouling rate,and cost (capital and/or operating);

c) calculating and storing said one or more of functions of interestcalculated in step b);

d) using some or all of the stored results from step 3c) with anoptimization algorithm to estimate a deformation that will improve theobjective function;

e) comparing the stored objective functions of interest until one orboth of the following conditions are met:

-   -   i) the objective function reaches a desirable local extrema; or    -   ii) the objective function ceases to change in the parametrized        direction.

Some objective function value, for example, pressure drop and erosionrate, at each evaluation stage in the process of finding the localextremum can be obtained via Computational Fluid Dynamics. If the changein transfer line cross-sections along the flow path is selected so thatthe calculated total pressure drop across the line decreases by about10% from the baseline condition made of standard components (i.e., wherethe ARQ is from about 1 to about 1.02 along the about 90% or about 80%of transfer line flow path) which is used as a comparison benchmark andthe erosion rate of the line is decreased by more than about 5% comparedto the baseline, calculated using a combination of structural finiteelement analysis software; computational fluid dynamics simulation ofthe flow rate and a geometry manipulating software that alters the shapeof the transfer line in a parametric fashion.

For example, the models will be run until the change in objectivefunction between successive iterations is less than about 10% or lessthan about 1%. In one embodiment, when compared to a baseline of aconventionally designed transfer line made of standard components, thepresent invention has a decrease in total pressure drop of over about10% and the subsequent erosion rate and fouling rate of the transferline is also affected and decreased when compared to the baselineconditions. This decrease is at least in the order of magnitude of thetotal pressure drop. In an optional embodiment, the fouling (e.g., cokedeposition) rate of the transfer line is also determined. The foulingrate as noted below is also a function of the metallurgy of the transferline and the surface coating in the transfer line.

The fouling rate for the transfer line exchanger and, optionally, thequench exchanger should be less than about 0.1 mg/cm²/hr, or less thanabout 0.07 mg/cm²/hr, or less than about 0.05 mg/cm²/hr, more or lessthan about 0.03 mg/cm²/hr, or less than about 0.02 mg/cm²/hr. The cokerate may be affected by a number of factors including the crosssectional shape of the transfer line exchanger and the metallurgy of thetransfer line exchanger. In one embodiment, for computer simulations,the metallurgy of the transfer line may be considered constant, andafter the preferred shape is determined, the metallurgy of the transferline may be selected.

In one embodiment, due to space constraints, the transfer line may“bend” prior to entering the quench exchanger. The radius of curvaturetaken at the inside of the curve in the transfer line is, for example,from about 1 to about 10 pipe inner diameters or from about 3 to about 5pipe inner diameters.

The transfer line and the quench exchanger may be constructed fromstainless steel. For example, the steel has a surface which tends tomitigate the formation of coke such as that disclosed in U.S. Pat. No.6,824,883 issued Nov. 30, 2004 to Benum et al. assigned to NOVAChemicals (International) S.A.

In one embodiment, the steel has a high nickel and chrome content.

In one embodiment, the stainless steel comprises from about 20 to about50, or from about 20 to about 38 weight % of chromium and at least about1.0 weight %, up to about 2.5 weight % or not more than about 2 weight %of manganese. The stainless steel should contain less than about 1.0, orless than about 0.9 weight % of niobium and less than about 1.5, or lessthan about 1.4 weight % of silicon. The stainless steel may furthercomprise from about 25 to about 50 weight % of nickel, from about 1.0 toabout 2.5 weight % of manganese and less than about 3 weight % oftitanium and all other trace metals, and carbon in an amount of lessthan about 0.75 weight %. The steel may comprise from about 25 to about50, or from about 30 to about 45 weight % nickel and, for example, lessthan about 1.4 weight % of silicon. The balance of the stainless steelis substantially iron. In a further embodiment, the stainless steel maycontain from about 0 up to about 6 weight %, or from about 3 to about 6weight % of aluminum.

In one embodiment, alloys may also be used, for example, nickel and/orcobalt based extreme austenitic high temperature alloys (HTAs). In oneembodiment, the alloys comprise a major amount of nickel or cobalt. Forexample, the high temperature nickel based alloys comprise from about 50to about 70, or from about 55 to about 65 weight % of Ni; from about 20to about 10 weight % of Cr; from about 20 to about 10 weight % of Co;and from about 5 to about 9 weight % of Fe and the balance one or moreof the trace elements noted below to bring the composition up to 100weight %. For example, the high temperature cobalt based alloys comprisefrom about 40 to about 65 weight % of Co; from about 15 to about 20weight % of Cr; from about 20 to about 13 weight % of Ni; less thanabout 4 weight % of Fe and the balance one or more trace elements as setout below and up to about 20 weight % of W. The sum of the componentsadding up to 100 weight %.

In another embodiment, newer alloys may be used which contain up toabout 12% Al, for example, less than about 7 weight %, or about 2.5 toabout 3 weight % aluminum as disclosed for example in U.S. Pat. No.7,278,828 issued Oct. 9, 2007 to Steplewski et al., assigned to GeneralElectric Company. For example, in the high cobalt and high nickelsteels, the aluminum may be present in an amount up to about 3 weight %,or between about 2.5 and about 3 weight %. In the high chrome highnickel alloys (e.g., about 13 to about 50, or about 20 to about 50,weight % of Cr and from about 20 to about 50 weight % of Ni), thealuminum content may range up to about 10, for example, less than about7, or from about 2 to about 7 weight %.

In some embodiments of the invention, the steel may further comprise anumber of trace elements including at least about 0.2 weight %, up toabout 3 weight % or about 1.0 weight %, up to about 2.5 weight % or notmore than about 2 weight % of manganese; from about 0.3 to about 2, orabout 0.8 to about 1.6 or less than about 1.9 weight % of Si; less thanabout 3, or less than about 2 weight % of titanium, niobium (forexample, less than about 2.0, or less than about 1.5 weight % ofniobium) and all other trace metals; and carbon in an amount of lessthan about 2.0 weight %. The trace elements are present in amounts sothat the composition of the steel totals 100 weight %.

In one embodiment, the transfer line (and the quench exchanger) may betreated to create a spinel surface on the internal surface. There appearto be a number of treatments which may create a spinel surface. Onetreatment, for example, comprises (i) heating the stainless steel in areducing atmosphere comprising from about 50 to about 100 weight % ofhydrogen and from about 0 to about 50 weight % of one or more inertgases at rate of about 100° C. to about 150° C. per hour to atemperature from about 800° C. to about 1100° C.; (ii) then subjectingthe stainless steel to an oxidizing environment having an oxidizingpotential equivalent to a mixture of from about 30 to about 50 weight %of air and from about 70 to about 50 weight % of one or more inert gasesat a temperature from about 800° C. to about 1100° C. for a period oftime from about 5 to about 40 hours; and (iii) cooling the resultingstainless steel to about room temperature at a rate of less than about200° C. per hour.

In one embodiment, this treatment should be carried out until there isan internal surface on the transfer line (and, optionally, the quenchexchanger) having a thickness greater than about 2 microns, for example,from about 2 to about 25, or from about 2 to about 15 microns or fromabout 2 to about 10 microns and substantially comprising a spinel of theformula Mn_(x)Cr_(3−x)O₄, where x is a number from about 0.5 to about 2,for example, from about 0.8 to about 1.2. In one embodiment, X is 1 andthe spinel has the formula MnCr₂O₄.

For example, the spinel surface covers not less than about 55%, or notless than about 60%, or not less than about 80%, or not less than about95% of the stainless steel.

In a further embodiment, there may be a chromia (Cr₂O₃) layerintermediate the surface spinel and the substrate stainless steel. Thechromia layer may have a thickness up to about 30 microns, generallyfrom about 5 to about 24, or from about 7 to about 15 microns. As notedabove, the spinel overcoats the chromia geometrical surface area. In oneembodiment, there may be very small portions of the surface which mayonly be chromia and do not have the spinel overlayer. In this sense, thelayered surface may be non-uniform. In one embodiment, the chromia layerunderlies or is adjacent not less than about 80, or not less than about95, most or not less than about 99% of the spinel.

In a further embodiment, the internal surface of the transfer line and,optionally, the quench exchanger may comprise from about 15 to about 85weight %, or from about 40 to about 60 weight % of compounds of theformula Mn_(x)Cr_(3−x)O₄, wherein x is from about 0.5 to about 2 andfrom about 85 to about 15 weight %, or from about 60 to about 40 weight% of oxides of Mn and Si selected from MnO, MnSiO₃, Mn₂SiO₄ and mixturesthereof provided that the surface contains less than about 5 weight % ofCr₂O₃.

The present invention will further be described by reference to thefollowing demonstrations, which are merely illustrative of the inventionand are not intended to be limiting.

Demonstration:

The present invention will now be demonstrated with reference to FIGS. 3and 4 and 7 and 8. FIGS. 3 and 4 are the conventional transfer lineexchanger and FIGS. 7 and 8 are a modified design in accordance with thepresent invention.

The finite element analysis software and computational fluid dynamicsoftware have been used to model NOVA Chemicals commercial ethylenecracking furnace piping at Joffre and Corunna. The models aresufficiently accurate to generally predict the commercial operation ofindustrial plants.

A numerical model of the conventional transfer line as shown in FIGS. 3and 4, a circular tapered tube with a 90° bend and trumpet-like diffuserconnecting to the heat exchanger tubesheet was created using acommercial finite element software program. A computational fluiddynamics program was also applied for the analysis of the conventionaltransfer line for gas at a temperature of greater than 600° C. and aflow rate of 3.97 Kg/s. The pressure drop and erosion rate weredetermined using ANSYS FLUENT software.

Using the shape deformation and optimization software Sculptor thecircular cross section of the conventional pipe computational ornumerical model was deformed into an asymmetric and arbitrary shapeindependently at several transverse planes of the original connectingpipe to generate a “deformed” shape based on a series of deformationparameters per section. The ARQ of the resulting sections having amaximum ARQ substantially greater than 1.02. The metallurgy of the pipewas maintained constant for these models. The pressure drop and erosionrate were also calculated for the “deformed” pipe.

The process was applied iteratively until no further improvements inpressure drop or erosion rate were found. The resulting geometry and ARQvalues are shown in FIG. 7 and FIG. 8.

Table 1 is a summary of representative data from the computer modeling.

TABLE 1 Simulation or Normalized Reduction in Iteration PressurePressure Normalized Reduction in Number Drop Drop Erosion Rate ErosionRate 1 (Base 1.0 0% 1.0 0% design in FIG. 1)  2 0.98 1% 0.99 1%  4 0.928% 0.96 4%  8 0.89 11% 0.94 6% 14 0.85 15% 0.90 10% 16 0.85 15% 0.89 11%21 0.82 18% 0.87 13%

Although the change in ARQ appears to be moderate, the resulting changein transfer line performance has been dramatic. In terms of time inservice until the unit needs to be decoked, the present demonstration ofthe invention increased the run time from a plant average of 90 days toan initial run of 290 days, or a 220% increase in run time. The factorsthat determine the end of a run include pressure drop across thetransfer line and temperature increase at the entrance of the exchanger.

The present invention has been described with reference to certaindetails of particular embodiments thereof. It is not intended that suchdetails be regarded as limitations upon the scope of the inventionexcept insofar as and to the extent that they are included in theaccompanying claims.

What is claimed is:
 1. A method to optimize one or more of the operatingcharacteristics selected from the group consisting of pressure drop,erosion rate, fouling rate, and cost (capital, operating, or both) of afixed industrial flow path defined by a continuous metal envelope,comprising:
 1. building a computational model comprising not less than5,000, computational cells of the portion of flow channel from 5% of thelength of the flow channel downstream of the inlet to from 5% of thelength of the flow channel upstream of the outlet of the initial designof said industrial flow path;
 2. using computer software that solves thefundamental laws of fluid and energy dynamics for each cell, simulatingand summing the results of the operation of the model design from step 1under the industrial pressure, temperature, and flow rate conditions ofoperation to verify one or more objective functions of interest; 3.iteratively a) deforming said computational model comprising not lessthan 5,000 computational cells so that the resulting ARQ is from 1.02 to1.15, where ARQ is defined as the ratio of aspect ratio (AR) toisoperimetric quotient (Q) of a section of the flow path perpendicularto the direction of flow; b) applying the same computer software as instep 2, that solves the fundamental laws of fluid and energy dynamicsfor each cell, simulating and summing the results of the operation ofthe deformed model from step 3a) under the industrial pressure,temperature, and flow rate conditions of operation used in step 2 topredict one or more objective functions of interest for the operation ofthe deformed model; c) storing the predicted results from step 3b); d)using some or all of the stored results from step 3c) with anoptimization algorithm to estimate a deformation that will improve theobjective function; e) repeating steps a), b), c), and d) until one orboth of the following conditions are met: i) the objective function ofinterest goes through a beneficial local extrema; or ii) the rate ofchange of all of the functions of interest starts to approach 0; whereinthe computational model has from 10,000 to 100,000 computational cells;wherein the flow path does not change by more than 7% over a 5% lengthof the flow path; wherein the ARQ at one or more sections over the flowpath is from 1.02 and 1.12; wherein the ARQ over 80% of the length ofthe flow path does not change by more than 5% over a 5% length of theflow path; wherein the calculated total pressure drop across the flowpath is decreased by not less than 10% compared to the calculatedpressure drop for a flow path having an ARQ along its length from 1.00to 1.02; wherein normalized calculated erosion rate of the flow path isdecreased by not less than 10% compared to the normalized erosion ratefor a flow path having an ARQ along its length from 1.00 to 1.02;wherein the flow path has an increasing cross sectional area in thedirection of flow such that the angle between the transverse normalvector and the flow path walls range from 0° to 85°; wherein the flowpath has a smooth curve in its longitudinal direction and a radius ofcurvature on the internal surface of the curve from unbound to half thevertical of the section radius; and wherein the flow path is defined bya continuous metal envelope comprising from 20 to 50 weight % ofchromium, 25 to 50 weight % of Ni, from 1.0 to 2.5 weight % of Mn, lessthan 1.0 weight % of niobium, less than 1.5 weight % of silicon, lessthan 3 weight % of titanium, and all other trace metals and carbon in anamount less than 0.75 weight %, and from 0 to 6 weight % of aluminum. 2.A method to optimize one or more of the operating characteristicsselected from the group consisting of pressure drop, erosion rate,fouling rate, and cost (capital, operating, or both) of a fixedindustrial flow path defined by a continuous metal envelope, wherein thecontinuous metal envelope comprises from 40 to 65 weight % of Co; from15 to 20 weight % of Cr; from 20 to 13 weight % of Ni; less than 4weight % of Fe and the balance of one or more trace elements and up to20 weight % of W the sum of the components adding up to 100 weight %,the method comprising:
 1. building a computational model comprising notless than 5,000, computational cells of the portion of flow channel from5% of the length of the flow channel downstream of the inlet to from 5%of the length of the flow channel upstream of the outlet of the initialdesign of said industrial flow path;
 2. using computer software thatsolves the fundamental laws of fluid and energy dynamics for each cell,simulating and summing the results of the operation of the model designfrom step 1 under the industrial pressure, temperature, and flow rateconditions of operation to verify one or more objective functions ofinterest;
 3. iteratively a) deforming said computational modelcomprising not less than 5,000 computational cells so that the resultingARQ is from 1.02 to 1.15, where ARQ is defined as the ratio of aspectratio (AR) to isoperimetric quotient (Q) of a section of the flow pathperpendicular to the direction of flow; b) applying the same computersoftware as in step 2, that solves the fundamental laws of fluid andenergy dynamics for each cell, simulating and summing the results of theoperation of the deformed model from step 3a) under the industrialpressure, temperature, and flow rate conditions of operation used instep 2 to predict one or more objective functions of interest for theoperation of the deformed model; c) storing the predicted results fromstep 3b); d) using some or all of the stored results from step 3c) withan optimization algorithm to estimate a deformation that will improvethe objective function; e) repeating steps a), b), c), and d) until oneor both of the following conditions are met: i) the objective functionof interest goes through a beneficial local extrema; or ii) the rate ofchange of all of the functions of interest starts to approach 0; whereinthe computational model has from 10,000 to 100,000 computational cells;wherein the flow path does not change by more than 7% over a 5% lengthof the flow path; wherein the ARQ at one or more sections over the flowpath is from 1.02 and 1.12; wherein the ARQ over 80% of the length ofthe flow path does not change by more than 5% over a 5% length of theflow path; wherein the calculated total pressure drop across the flowpath is decreased by not less than 10% compared to the calculatedpressure drop for a flow path having an ARQ along its length from 1.00to 1.02; wherein normalized calculated erosion rate of the flow path isdecreased by not less than 10% compared to the normalized erosion ratefor a flow path having an ARQ along its length from 1.00 to 1.02;wherein the flow path has an increasing cross sectional area in thedirection of flow such that the angle between the transverse normalvector and the flow path walls range from 0° to 85°; and wherein theflow path has a smooth curve in its longitudinal direction and a radiusof curvature on the internal surface of the curve from unbound to halfthe vertical of the section radius.
 3. A method to optimize one or moreof the operating characteristics selected from the group consisting ofpressure drop, erosion rate, fouling rate, and cost (capital, operating,or both) of a fixed industrial flow path defined by a continuous metalenvelope, wherein the flow path is defined by a continuous metalenvelope comprising from 55 to 65 weight % of Ni; from 20 to 10 weight %of Cr; from 20 to 10 weight % of Co; and from 5 to 9 weight % of Fe, andthe balance of one or more-trace elements, the method comprising: 1.building a computational model comprising not less than 5,000,computational cells of the portion of flow channel from 5% of the lengthof the flow channel downstream of the inlet to from 5% of the length ofthe flow channel upstream of the outlet of the initial design of saidindustrial flow path;
 2. using computer software that solves thefundamental laws of fluid and energy dynamics for each cell, simulatingand summing the results of the operation of the model design from step 1under the industrial pressure, temperature, and flow rate conditions ofoperation to verify one or more objective functions of interest; 3.iteratively a) deforming said computational model comprising not lessthan 5,000 computational cells so that the resulting ARQ is from 1.02 to1.15, where ARQ is defined as the ratio of aspect ratio (AR) toisoperimetric quotient (Q) of a section of the flow path perpendicularto the direction of flow; b) applying the same computer software as instep 2, that solves the fundamental laws of fluid and energy dynamicsfor each cell, simulating and summing the results of the operation ofthe deformed model from step 3a) under the industrial pressure,temperature, and flow rate conditions of operation used in step 2 topredict one or more objective functions of interest for the operation ofthe deformed model; c) storing the predicted results from step 3b); d)using some or all of the stored results from step 3c) with anoptimization algorithm to estimate a deformation that will improve theobjective function; e) repeating steps a), b), c), and d) until one orboth of the following conditions are met: i) the objective function ofinterest goes through a beneficial local extrema; or ii) the rate ofchange of all of the functions of interest starts to approach 0; whereinthe computational model has from 10,000 to 100,000 computational cells;wherein the flow path does not change by more than 7% over a 5% lengthof the flow path; wherein the ARQ at one or more sections over the flowpath is from 1.02 and 1.12; wherein the ARQ over 80% of the length ofthe flow path does not change by more than 5% over a 5% length of theflow path; wherein the calculated total pressure drop across the flowpath is decreased by not less than 10% compared to the calculatedpressure drop for a flow path having an ARQ along its length from 1.00to 1.02; wherein normalized calculated erosion rate of the flow path isdecreased by not less than 10% compared to the normalized erosion ratefor a flow path having an ARQ along its length from 1.00 to 1.02;wherein the flow path has an increasing cross sectional area in thedirection of flow such that the angle between the transverse normalvector and the flow path walls range from 0° to 85°; and wherein theflow path has a smooth curve in its longitudinal direction and a radiusof curvature on the internal surface of the curve from unbound to halfthe vertical of the section radius.